Faster Low-rank Approximation using Adaptive Gap-based Preconditioning

Salon des Refusés, 2016.

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Abstract:

We propose a method for rank $k$ approximation to a given input matrix $X \in \mathbb{R}^{d \times n}$ which runs in time \[ \tilde{O} \left(d ~\cdot~ \min\left\{n + \tilde{sr}(X) \,G^{-2}_{k,p+1}\ ,\ n^{3/4}\, \tilde{sr}(X)^{1/4} \,G^{-1/2}_{k,p+1} \right\} ~\cdot~ \text{poly}(p)\right) ~, \] where $p>k$, $\tilde{sr}(X)$ is related to ...More

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